Dissertations / Theses on the topic 'Random motion in random media'
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Jaruwatanadilok, Sermsak. "Optical wave propagation and imaging in descrete random media /." Thesis, Connect to this title online; UW restricted, 2003. http://hdl.handle.net/1773/5839.
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Wu, Ying. "Effective medium theory for elastic metamaterials and wave propagation in strongly scattered random elastic media /." View abstract or full-text, 2008. http://library.ust.hk/cgi/db/thesis.pl?PHYS%202008%20WU.
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Sposini, Vittoria. "A numerical study of fractional diffusion through a Langevin approach in random media." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amslaurea.unibo.it/12494/.
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The study of Brownian motion has a long history and involves many different formulations. All these formulations show two fundamental common results: the mean square displacement of a diffusing particle scales linearly with time and the probability density function is a Guassian distribution.
However standard diffusion is not universal. In literature there are numerous experimental measurements showing non linear diffusion in many fields including physics, biology, chemistry, engineering, astrophysics and others. This behavior can have different physical origins and has been found to occur frequently in spatially disordered systems, in turbulent fluids and plasmas, and in biological media with traps, binding sites or macro-molecular crowding.
Langevin approach describes the Brownian motion in terms of a stochastic differential equation.
The process of diffusion is driven by two physical parameters, the relaxation or correlation time tau and the velocity diffusivity coefficient Dv.
An extension of the classical Langevin approach by means of a population of tau and Dv is here considered to generate a fractional dynamics. This approach supports the idea that fractional diffusion in complex media results from Gaussian processes with random parameters, whose randomness is due to the medium complexity. A statistical characterization of the complex medium in which the diffusion occurs is realized deriving the distributions of these parameters.
Specific populations of tau and Dv lead to particular fractional diffusion processes.
This approach allows for preserving the classical Brownian motion as basis and it is promising to formulate stochastic processes for biological systems that show complex dynamics characterized by fractional diffusion.
A numerical study of this new alternative approach represents the core of the present thesis.
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Wong, Chik Him. "A theoretical study on the static and dynamic transport properties of classical wave in 1D random media /." View abstract or full-text, 2007. http://library.ust.hk/cgi/db/thesis.pl?PHYS%202007%20WONG.
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Meng, Hsin-fei. "Superfluidity and random media." Thesis, Massachusetts Institute of Technology, 1993. http://hdl.handle.net/1721.1/103194.
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Lessa, Pablo. "Brownian motion on stationary random manifolds." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2014. http://tel.archives-ouvertes.fr/tel-00959923.
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On introduit le concept d'une variété aléatoire stationnaire avec l'objectif de traiter de façon unifiée les résultats sur les variétés avec un group d'isométries transitif, les variétés avec quotient compact, et les feuilles génériques d'un feuilletage compact. On démontre des inégalités entre la vitesse de fuite, l'entropie du mouvement brownien et la croissance de volume de la variété aléatoire, en généralisant des résultats d'Avez, Kaimanovich, et Ledrappier. Dans la deuxième partie on démontre que la fonction feuille d'un feuilletage compact est semicontinue, en obtenant comme conséquences le théorème de stabilité local de Reeb, une partie du théorème de structure local pour les feuilletages à feuilles compactes d'Epstein, et un théorème de continuité d'Álvarez et Candel.
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Tsay, Jhishen. "Wave scattering in random media." Diss., The University of Arizona, 1991. http://hdl.handle.net/10150/185541.
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We study the scattering theory for the descrete Schrodinger equation with a random potential having large finite support. We consider in one dimension a wave packet incoming from one side of the disordered section. We prove that the transmission of a wave packet is improbable if the disordered section is large, and that a fluctuation deep within the disordered section has a very small effect on the scattering of wave packets. The scattering theory for the discrete random Schrodinger equation in a strip in two dimensions is also considered. We derive large deviation bounds on the elements of the transmission matrix uniform in the energy parameter. These uniform bounds are used to show that the probability of a significant portion of a wave packet is transmitted is small as the length of the disordered section becomes large. We also study the time delay in potential scattering. We consider the situation when the potential becomes a white noise. The time delay is related to the energy derivative of the phase shift. We derive stochastic differential equations for the phase shift and the frequency derivative of the phase shift. We find that there is no time delay in the low frequency limit. However in the high frequency limit we find the time delay is a random function of the depth of the disordered section.
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Tseng, David Tai Hee. "Restoration of random motion degraded sonar images." Thesis, University of British Columbia, 1986. http://hdl.handle.net/2429/26338.
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The problem of sonar images degraded by wave-induced random ship motion and their restoration by filtering methods is investigated. The nature of the random motion is examined in detail, and a model is set up to describe its power spectrum in terms of the sea spectrum and the ship's receptance. A sonar measurement formula and its approximated form is derived. It is shown that the approximation represents a signal with additive coloured noise process. The signal is the measured seafloor profile and is approximated by a first-order Markov process. Several filters are proposed: Kalman Filter, Recursive Least Squares Interpolating (RLSI) Filter, and Adaptive ARMA Filter. In addition, Fast Estimation Algorithm and Adaptive Algorithm are introduced to determine unknown parameters in the Kalman Filter. Simulation results are generated using these filters. Performances are found to be strongly dependent on both signal and noise characteristics, with the exception of the RLSI Filter, which is relatively independent of wind speed, the main noise parameter. Computational complexities, estimation delay and convergence rates associated with the various filters are also examined. Finally, Extended Kalman Filter and Self-Tuning Filter are proposed as possible candidates for dealing with non-stationary, time-varying degradation problem.Applied Science, Faculty of
Electrical and Computer Engineering, Department of
Graduate
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Uldry, Anne-Christine. "Two-particle excitations in random media." Thesis, University of Oxford, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.270724.
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Schwartz, Chaim. "Probing Random Media with Singular Waves." Doctoral diss., University of Central Florida, 2006. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/4252.
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In recent years a resurgence of interest in wave singularities (of which optical vortices are a prominent example), light angular momentum and the relations between them has occurred. Many applications in various areas of linear and non-linear optics have been based on studying effects related to angular momentum and optical vortices. This dissertation examines the use of such wave singularities for studying the light propagation in highly inhomogeneous media and the relationship to angular momentum transfer. Angular momentum carried by light can be, in many cases, divided in two terms. The first one relates to the polarization of light and can be associated, in the quantum description, to the spin of a photon. The second is determined by the electromagnetic field distribution and, in analogy to atomic physics, is associated with the orbital angular momentum (OAM) of a photon. Under the paraxial approximation appropriate for the case of beam propagation, the two terms do not couple. However, each of them can be modified by the interaction with different media in which the light propagates through processes which involve angular momentum exchange. The decoupling of spin and orbital parts of light angular momentum can not, in general, be assumed for non paraxial propagation in turbid media, especially when backscattering is concerned. In Chapter 3 of this dissertation, scattering effects on angular momentum of light are discussed both for the single and multiple scattering processes. It is demonstrated for the first time that scattering from a spherically symmetric scattering potential, couples the spin and the OAM such that the total angular momentum flux density in conserved in every direction. Remarkably, the conservation of angular momentum occurs also for some classes of multiple scattering trajectories and this phenomenon manifests itself in ubiquitous polarization patterns observed in back-scattering from turbid media. It is newly shown in this dissertation that the polarization patterns a result of OAM carrying optical vortices which have a geometrical origin. These geometrical phase vortices are analyzed using the helicity space approach for optical geometrical phase (Berry phase). This approach, introduced in the con- text of random media, elucidates several aspects specific to propagation in helicity preserving and non-preserving scattering trajectories. Another aspect of singular waves interaction with turbid media relates to singularities embedded in the incident waves. Chapter 4 of the dissertation discusses how the phase distribution associated with an optical vortex leads to changes in the spatial correlations of the electromagnetic field. This change can be used to control the properties of the effect of enhanced backscattering in a way which allows inferring the optical properties of the medium. A detailed theoretical and experimental study of this effect is presented here for the first time for both double-pass geometries and diffusive media. It is also demonstrated that this novel experimental technique can be used to determine the optical properties of turbid media and, moreover, it permits to sense the depth of reflective inclusions in opaque media. When considering a regime of weakly inhomogeneous media, the paraxial approximation is still valid and therefore the spin and OAM do not couple. If, In addition, the medium is optically isotropic then the polarization is not affected. However, when the medium is non-axially symmetric for any specific realization, the OAM does change as a result of interaction with the medium. This effect can be studied using a newly developed method of coherent modes coupling which is presented in Chapter 5. This approach allows studying the power spread across propagating modes which carry different orbital angular momentum. The powerful concept of coherent modes coupling can be applied to fully coherent, fully polarized sources as well to partially coherent, partially polarized ones. An example of this scattering regime is atmospheric turbulence and the propagation through turbulence is thoroughly examined in Chapter 5. The results included in this dissertation are of fundamental relevance for a variety of applications which involves probing different types of random media. Such applications include remote sensing in atmospheric and maritime environments, optical techniques for biomedical diagnostics, optical characterization procedures in material sciences and others.Ph.D.
Other
Optics and Photonics
Optics
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Ortmann, Janosch. "Random matrices, large deviations and reflected Brownian motion." Thesis, University of Warwick, 2011. http://wrap.warwick.ac.uk/50020/.
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In this thesis we present results in large deviations theory, free probability and the theory of reflected Brownian motion. We study the large deviations behaviour of the block structure of a non-crossing partition chosen uniformly at random. This allows us to apply the free momentcumulant formula of Speicher to express the spectral radius of a non-commutative random variable in terms of its free cumulants. Next the distributions of three quadratic functionals of the free Brownian bridge are studied: the square norm, the signature and the Lévy area of the free Brownian bridge. We introduce two representation of the free Brownian bridge as series involving free semicircular variables, analogous to classical results due to Lévy and Kac. The latter representation extends to all semicircular processes. For each of the three quadratic functionals we give the R-transform, from which we extract information about the distribution, including free infinite divisibility and smoothness of the density. We also apply our result about the spectral radius to compute the maximum of the support for Lévy area and square norm. In both cases we obtain implicit equations. The final chapter of the thesis is devoted to the study of a generalisation of reflected Brownian motion (RBM) in a polyhedral domain. This is motivated by recent developments in the theory of directed polymer and percolation models, in which existence of an invariant measure in product form plays a role. Informally, RBM is defined by running a standard Brownian motion in the polyhedral domain and giving it a singular drift whenever it hits one of the boundaries, kicking the process back into the interior. Our process is obtained by replacing this singular drift by a continuous one, involving a continuous potential. RBM has an invariant measure in product form if and only if a certain skew-symmetry condition holds. We show that this result extends to our generalisation. Applications include examples motivated by queueing theory, Brownian motion with rank-dependent drift and a process with close connections to the δ-Bose gas.
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LaGatta, Tom. "Geodesics of Random Riemannian Metrics." Diss., The University of Arizona, 2010. http://hdl.handle.net/10150/193749.
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We introduce Riemannian First-Passage Percolation (Riemannian FPP) as a new model of random differential geometry, by considering a random, smooth Riemannian metric on R^d . We are motivated in our study by the random geometry of first-passage percolation (FPP), a lattice model which was developed to model fluid flow through porous media. By adapting techniques from standard FPP, we prove a shape theorem for our model, which says that large balls under this metric converge to a deterministic shape under rescaling. As a consequence, we show that smooth random Riemannian metrics are geodesically complete with probability one.In differential geometry, geodesics are curves which locally minimize length. They need not do so globally: consider great circles on a sphere. For lattice models of FPP, there are many open questions related to minimizing geodesics; similarly, it is interesting from a geometric perspective when geodesics are globally minimizing. In the present study, we show that for any fixed starting direction v, the geodesic starting from the origin in the direction v is not minimizing with probability one. This is a new result which uses the infinitesimal structure of the continuum, and for which there is no equivalent in discrete lattice models of FPP.
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Lienau, Karsten. "Spectral concentration for high contrast random media." [S.l. : s.n.], 1999. http://deposit.ddb.de/cgi-bin/dokserv?idn=956684971.
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Ababou, R. (Rachid). "Three-dimensional flow in random porous media." Thesis, Massachusetts Institute of Technology, 1988. http://hdl.handle.net/1721.1/14675.
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Sousi, Perla. "Collisions and detection for random walks and Brownian motion." Thesis, University of Cambridge, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.609815.
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Berchtold, Maik. "Modelling of random porous media using Minkowski-functionals /." Zürich : ETH, 2007. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=17549.
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McLean, Alan Stuart. "Transfer matrices and image transport in random media." Thesis, Imperial College London, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.307659.
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Costaouec, Ronan, and Ronan Costaouec. "Numerical methods for homogenization : applications to random media." Phd thesis, Université Paris-Est, 2011. http://pastel.archives-ouvertes.fr/pastel-00674957.
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In this thesis we investigate numerical methods for the homogenization of materials the structures of which, at fine scales, are characterized by random heterogenities. Under appropriate hypotheses, the effective properties of such materials are given by closed formulas. However, in practice the computation of these properties is a difficult task because it involves solving partial differential equations with stochastic coefficients that are additionally posed on the whole space. In this work, we address this difficulty in two different ways. The standard discretization techniques lead to random approximate effective properties. In Part I, we aim at reducing their variance, using a well-known variance reduction technique that has already been used successfully in other domains. The works of Part II focus on the case when the material can be seen as a small random perturbation of a periodic material. We then show both numerically and theoretically that, in this case, computing the effective properties is much less costly than in the general case
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Miller, Sarah Judith. "Scattering of multi-frequency waves by random media." Thesis, University of Cambridge, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.256408.
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Park, Samuel. "Radiation transport in multiphase and spatially random media." Thesis, Imperial College London, 2016. http://hdl.handle.net/10044/1/45051.
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An important class of problems within radiation (e.g. neutrons, photons) transport are those in which the radiation migrates through a medium which has a random or stochastic composition. The uncertain medium composition introduces an uncertainty in the radiation angular/scalar flux, current, reaction rates and other quantities of interest. Stochastic media play an important role within radiation transport and have numerous applications such as radiation shielding, nuclear criticality assessment, as well as radiative transfer in clouds, stellar atmospheres and plasma physics. Stochastic radiation transport problems reduce to treating the adsorption, scatter and other macroscopic cross-section data as spatially correlated random fields. Several methods for the treatment of these uncertain-ties have been proposed however they are limited in their scope and computational efficiency. Multiphase and spatially random media are often characterised by non-Gaussian random fields which are much more challenging to model than Gaussian random fields. This thesis aims to investigate, develop and implement mathematically rigorous computational algorithms that are more efficient than the current methods for solving radiation transport with multiphase and spatially random media. In particular this thesis applies iso-probabilistic (e.g. Nataf) transforms to transform Gaussian random fields into non-Gaussian random fields. This approach enables the use of optimal spectral stochastic representations, such as the Karhunen-Loève and generalized polynomial chaos methods, to be used to simulate non-Gaussian random fields. This thesis also describes the verification of these iso-probabilistic spectral stochastic projection methods against standard radiation transport in random media benchmarks, such as the widely used Adams-Levermore-Pomraning benchmark. This thesis is the first time the general Nataf method has been applied to model radiation transport through multiphase and spatially random media.
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Li, Chenfeng. "Stochastic finite element modelling of elementary random media." Thesis, Swansea University, 2006. https://cronfa.swan.ac.uk/Record/cronfa42770.
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Following a stochastic approach, this thesis presents a numerical framework for elastostatics of random media. Firstly, after a mathematically rigorous investigation of the popular white noise model in an engineering context, the smooth spatial stochastic dependence between material properties is identified as a fundamental feature of practical random media. Based on the recognition of the probabilistic essence of practical random media and driven by engineering simulation requirements, a comprehensive random medium model, namely elementary random media (ERM), is consequently defined and its macro-scale properties including stationarity, smoothness and principles for material measurements are systematically explored. Moreover, an explicit representation scheme, namely the Fourier-Karhunen-Loeve (F-K-L) representation, is developed for the general elastic tensor of ERM by combining the spectral representation theory of wide-sense stationary stochastic fields and the standard dimensionality reduction technology of principal component analysis. Then, based on the concept of ERM and the F-K-L representation for its random elastic tensor, the stochastic partial differential equations regarding elastostatics of random media are formulated and further discretized, in a similar fashion as for the standard finite element method, to obtain a stochastic system of linear algebraic equations. For the solution of the resulting stochastic linear algebraic system, two different numerical techniques, i.e. the joint diagonalization solution strategy and the directed Monte Carlo simulation strategy, are developed. Original contributions include the theoretical analysis of practical random medium modelling, establishment of the ERM model and its F-K-L representation, and development of the numerical solvers for the stochastic linear algebraic system. In particular, for computational challenges arising from the proposed framework, two novel numerical algorithms are developed: (a) a quadrature algorithm for multidimensional oscillatory functions, which reduces the computational cost of the F-K-L representation by up to several orders of magnitude; and (b) a Jacobi-like joint diagonalization solution method for relatively small mesh structures, which can effectively solve the associated stochastic linear algebraic system with a large number of random variables.
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Costaouec, Ronan. "Numerical methods for homogenization : applications to random media." Thesis, Paris Est, 2011. http://www.theses.fr/2011PEST1012/document.
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Le travail de cette thèse a porté sur le développement de techniques numériques pour l'homogénéisation de matériaux présentant à une petite échelle des hétérogénéités aléatoires. Sous certaines hypothèses, la théorie mathématique de l'homogénéisation stochastique permet d'expliciter les propriétés effectives de tels matériaux. Néanmoins, en pratique, la détermination de ces propriétés demeure difficile. En effet, celle-ci requiert la résolution d'équations aux dérivées partielles stochastiques posées sur l'espace tout entier. Dans cette thèse, cette difficulté est abordée de deux manières différentes. Les méthodes classiques d'approximation conduisent à approcher les propriétés effectives par des quantités aléatoires. Réduire la variance de ces quantités est l'objectif des travaux de la Partie I. On montre ainsi comment adapter au cadre de l'homogénéisation stochastique une technique de réduction de variance déjà éprouvée dans d'autres domaines. Les travaux de la Partie II s'intéressent à des cas pour lesquels le matériau d'intérêt est considéré comme une petite perturbation aléatoire d'un matériau de référence. On montre alors numériquement et théoriquement que cette simplification de la modélisation permet effectivement une réduction très importante du coût calculIn this thesis we investigate numerical methods for the homogenization of materials the structures of which, at fine scales, are characterized by random heterogenities. Under appropriate hypotheses, the effective properties of such materials are given by closed formulas. However, in practice the computation of these properties is a difficult task because it involves solving partial differential equations with stochastic coefficients that are additionally posed on the whole space. In this work, we address this difficulty in two different ways. The standard discretization techniques lead to random approximate effective properties. In Part I, we aim at reducing their variance, using a well-known variance reduction technique that has already been used successfully in other domains. The works of Part II focus on the case when the material can be seen as a small random perturbation of a periodic material. We then show both numerically and theoretically that, in this case, computing the effective properties is much less costly than in the general case
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Du, Xiangdong 1967. "Scaling laws in permeability and thermoelasticity of random media." Thesis, McGill University, 2006. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=102973.
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Under consideration is the finite-size scaling of two thermomechanical responses of random heterogeneous materials. Stochastic mechanics is applied here to the modeling of heterogeneous materials in order to construct the constitutive relations. Such relations (e.g. Hooke's Law in elasticity or Fourier's Law in heat transfer) are well-established under spatial homogeneity assumption of continuum mechanics, where the Representative Volume Element (RVE) is the fundamental concept. The key question is what is the size L of RVE? According to the separation of scales assumption, L must be bounded according to d<L<<LMacro where d is the microscale (or average size of heterogeneity), and LMacro is the macroscale of a continuum mechanics problem. Statistically, for spatially ergodic heterogeneous materials, when the mesoscale is equal to or bigger than the scale of the RVE, the elements of the material can be considered homogenized. In order to attain the said homogenization, two conditions must be satisfied: (a) the microstructure's statistics must be spatially homogeneous and ergodic; and (b) the material's effective constitutive response must be the same under uniform boundary conditions of essential (Dirichlet) and natural (Neumann) types.In the first part of this work, the finite-size scaling trend to RVE of the Darcy law for Stokesian flow is studied for the case of random porous media, without invoking any periodic structure assumptions, but only assuming the microstructure's statistics to be spatially homogeneous and ergodic. By analogy to the existing methodology in thermomechanics of solid random media, the Hill-Mandel condition for the Darcy flow velocity and pressure gradient fields was first formulated. Under uniform essential and natural boundary conditions, two variational principles are developed based on minimum potential energy and complementary energy. Then, the partitioning method was applied, leading to scale dependent hierarchies on effective (RVE level) permeability. The proof shows that the ensemble average of permeability has an upper bound under essential boundary conditions and a lower bound under uniform natural boundary conditions.
To quantitatively assess the scaling convergence towards the RVE, these hierarchical trends were numerically obtained for various porosities of random disk systems, where the disk centers were generated by a planar Poisson process with inhibition. Overall, the results showed that the higher the density of random disks---or, equivalently, the narrower the micro-channels in the system---the smaller the size of RVE pertaining to the Darcy law.
In the second part of this work, the finite-size scaling of effective thermoelastic properties of random microstructures were considered from Statistical to Representative Volume Element (RVE). Similarly, under the assumption that the microstructure's statistics are spatially homogeneous and ergodic, the SVE is set-up on a mesoscale, i.e. any scale finite relative to the microstructural length scale. The Hill condition generalized to thermoelasticity dictates uniform essential and natural boundary conditions, which, with the help of two variational principles, led to scale dependent hierarchies of mesoscale bounds on effective (RVE level) properties: thermal expansion strain coefficient and stress coefficient, effective stiffness, and specific heats. Due to the presence of a non-quadratic term in the energy formulas, the mesoscale bounds for the thermal expansion are more complicated than those for the stiffness tensor and the heat capacity. To quantitatively assess the scaling trend towards the RVE, the hierarchies are computed for a planar matrix-inclusion composite, with inclusions (of circular disk shape) located at points of a planar, hard-core Poisson point field. Overall, while the RVE is attained exactly on scales infinitely large relative to microscale, depending on the microstructural parameters, the random fluctuations in the SVE response become very weak on scales an order of magnitude larger than the microscale, thus already approximating the RVE.
Based on the above studies, further work on homogenization of heterogeneous materials is outlined at the end of the thesis.
Keywords: Representative Volume Element (RVE), heterogeneous media, permeability, thermal expansion, mesoscale, microstructure.
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Ooi, Kean Hong. "Light scattering in discrete random media and related materials." Thesis, University of Southampton, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.323917.
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Lampshire, Gregory B. "Review of random media homogenization using effective medium theories." Thesis, Virginia Tech, 1992. http://hdl.handle.net/10919/40659.
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Calculation of propagation constants in particulate matter is an important aspect of wave propagation analysis in engineering disciplines such as satellite comnlunication, geophysical exploration, radio astronomy and material science. It is important to understand why different propagation constants produced by different theories are not applicable to a particular problem. Homogenization of the random media using effective medium theories yields the effective propagation constants by effacing the particulate, microscopic nature of the medium. The Maxwell-Gamet and Bruggeman effective medium theories are widely used but their limitations are not always well understood.
In this thesis, some of the more complex homogenization theories will only be partially derived or heuristically constructed in order to avoid unnecessary mathematical complexity which does not yield additional physical insight. The intent of this thesis is to elucidate the nature of effective medium theories, discuss the theories' approximations and gain a better global understanding of wave propagation equations. The focus will be on the Maxwell-Garnet and Bruggeman theories because they yield simple relationships and therefore serve as anchors in a sea of myriad approximations.
Master of Science
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Pack, Jeong-Ki. "Numerical simulation of optical wave propagation through random media." Diss., Virginia Polytechnic Institute and State University, 1988. http://hdl.handle.net/10919/82642.
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The propagation of optical plane waves through a one-dimensional Gaussian phase screen and a two-dimensional Gaussian extended medium are simulated numerically, and wave statistics are calculated from the data obtained by the numerical simulation. For instantaneous realization of a random medium, a simplified version of the random-motion model [77] is used, and for wave-propagation calculation the wave-kinetic numerical method and/or the angular-spectral representation of the Huygens-Fresnel diffraction formula are used. For the wave-kinetic numerical method, several different levels of approximations are introduced, and the region of validity of those approximations is studied by single-realization calculations. Simulation results from the wave-kinetic numerical method are compared, either with those from the existing analytical expressions for the phase-screen problem, or with those from the Huygens-Fresnel diffraction formula for the extended-medium problem. Excellent agreement has been observed. Extension to two-dimensional media with the power-law spectrum or three-dimensional problems is straight-forward. We may also deal with space-time correlations using, for example, Taylor's frozen-in hypothesis.Ph. D.
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Lam, Chi Ming. "Theoretical and numerical studies of electromagnetic wave scattering from random media with random rough surfaces and discrete particles /." Thesis, Connect to this title online; UW restricted, 1992. http://hdl.handle.net/1773/5982.
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Schriemer, Henry P. "Ballistic and diffusive transport of acoustic waves in random media." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq23659.pdf.
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Wan, Yanyi. "Static and dynamic transport properties of 2D elastic random media /." View abstract or full-text, 2007. http://library.ust.hk/cgi/db/thesis.pl?PHYS%202007%20WAN.
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White, John D. H. "A random signal ultrasonic test system for highly attenuating media." Thesis, Keele University, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.315234.
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Cheng, Chung-Chieh. "Propagation of transverse optical coherence in random multiple-scattering media /." view abstract or download file of text, 1999. http://wwwlib.umi.com/cr/uoregon/fullcit?p9955916.
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Thesis (Ph. D.)--University of Oregon, 1999.Typescript. Includes vita and abstract. Includes bibliographical references (leaves 131-135). Also available for download via the World Wide Web; free to University of Oregon users. Address: http://wwwlib.umi.com/cr/uoregon/fullcit?p9955916.
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Kim, Arnold D. "Optical pulse propagation, diffusion and depolarization in discrete random media /." Thesis, Connect to this title online; UW restricted, 2000. http://hdl.handle.net/1773/6770.
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Goodman, Matthew R. "Properties of Stochastic Flow and Permeability of Random Porous Media." Thesis, The University of Arizona, 2010. http://hdl.handle.net/10150/193422.
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Thermosolutal fluid flow has a strong influence on the evolution of solidification microstructures. While porous media theory and volume-averaged permeability relations give a basis to quantify these phenomena, traditional methods of permeability estimation used for random porous media fail to adequately characterize the full relation of microstructural morphology to volume-average permeability. Most significantly, the link between microstructural parameters and permeability is treated as a deterministic function at all scales, ignoring the variability inherent in porous media.The variation in permeability inherent to random porous media is investigated by the numerical solution of Stokes equations on an ensemble of porous media, which represent of many scales of sampling and morphological character. Based on volume-averaging and statistical treatment, the stochastic character of tensoral permeability in porous media is numerically investigated. Quantification of permeability variation and autocorrelation structure are presented as conditions, which future realistic stochastic permeability fields must respect.
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Allen, Andrew. "A Random Walk Version of Robbins' Problem." Thesis, University of North Texas, 2018. https://digital.library.unt.edu/ark:/67531/metadc1404568/.
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Robbins' problem is an optimal stopping problem where one seeks to minimize the expected rank of their observations among all observations. We examine random walk analogs to Robbins' problem in both discrete and continuous time. In discrete time, we consider full information and relative ranks versions of this problem. For three step walks, we give the optimal stopping rule and the expected rank for both versions. We also give asymptotic upper bounds for the expected rank in discrete time. Finally, we give upper and lower bounds for the expected rank in continuous time, and we show that the expected rank in the continuous time problem is at least as large as the normalized asymptotic expected rank in the full information discrete time version.
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Falconer, Steven. "Subdiffusive transport in non-homogeneous media and nonlinear fractional equations." Thesis, University of Manchester, 2015. https://www.research.manchester.ac.uk/portal/en/theses/subdiffusive-transport-in-nonhomogeneous-media-and-nonlinear-fractional-equations(a695fe6e-02d2-4fa1-b90b-6a57505973fc).html.
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Adil, Adam Mohamed. "Simulation of ship motion and deck-wetting due to steep random seas." Thesis, Texas A&M University, 2004. http://hdl.handle.net/1969.1/1386.
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The extreme motion and load of ships have been assessed using a linear frequency domain method or a linear energy spectral method and RAOs, which may be too approximate to be used for estimation of ship motion in severest seas. The new technology uses simulation in the time domain to deal with the non-linear responses to the random seas. However, the current simulation technique has been successful only up to the sea state of 7 (high seas), defined by the significant wave height of 9 meters. The above cannot provide the extreme wave loads and motions for seas higher than the sea state 7. The ultimate goal of this work would be to develop a new technique that can simulate responses to the seas of states 8 and 9. The objective of the present study is to simulate the vertical relative motion and wave topping of a moored ship in the time domain by varying the significant wave heights. The analysis was able to predict with a fair accuracy the relative motion characteristics of a freely floating body in the head and beam sea conditions. The resonance aspects and its significance in the overall response are also analyzed.
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Lin, Tongling. "Path probability and an extension of least action principle to random motion." Phd thesis, Université du Maine, 2013. http://tel.archives-ouvertes.fr/tel-00795600.
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The present thesis is devoted to the study of path probability of random motion on the basis of an extension of Hamiltonian/Lagrangian mechanics to stochastic dynamics. The path probability is first investigated by numerical simulation for Gaussian stochastic motion of non dissipative systems. This ideal dynamical model implies that, apart from the Gaussian random forces, the system is only subject to conservative forces. This model can be applied to underdamped real random motion in the presence of friction force when the dissipated energy is negligible with respect to the variation of the potential energy. We find that the path probability decreases exponentially with increasing action, i.e., P(A) ~ eˉγA, where γ is a constant characterizing the sensitivity of the action dependence of the path probability, the action is given by A = ∫T0 Ldt, a time integral of the Lagrangian L = K-V over a fixed time period T, K is the kinetic energy and V is the potential energy. This result is a confirmation of the existence of a classical analogue of the Feynman factor eiA/ħ for the path integral formalism of quantum mechanics of Hamiltonian systems. The above result is then extended to real random motion with dissipation. For this purpose, the least action principle has to be generalized to damped motion of mechanical systems with a unique well defined Lagrangian function which must have the usual simple connection to Hamiltonian. This has been done with the help of the following Lagrangian L = K - V - Ed, where Ed is the dissipated energy. By variational calculus and numerical simulation, we proved that the action A = ∫T0 Ldt is stationary for the optimal paths determined by Newtonian equation. More precisely, the stationarity is a minimum for underdamped motion, a maximum for overdamped motion and an inflexion for the intermediate case. On this basis, we studied the path probability of Gaussian stochastic motion of dissipative systems. It is found that the path probability still depends exponentially on Lagrangian action for the underdamped motion, but depends exponentially on kinetic action A = ∫T0 Kdt for the overdamped motion.
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Lintz, William A. "Radio frequency signal reception via distributed wirelessly networked sensors under random motion." Monterey, Calif. : Naval Postgraduate School, 2009. http://edocs.nps.edu/npspubs/scholarly/dissert/2009/Sep/09Sep%5FLintz%5FPhD.pdf.
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Dissertation (Ph.D. in Electrical Engineering)--Naval Postgraduate School, September 2009.Dissertation supervisor: McEachen, John ; Tummala, Murali. "September 2009." Description based on title screen as viewed on November 5, 2009. Author(s) subject terms: Sensor Networks, Beamforming, Random Motion, Orientation Includes bibliographical references (p. 197-203). Also available in print.
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Bender, Martin. "Limit theorems for generalizations of GUE random matrices." Doctoral thesis, KTH, Matematik (Inst.), 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4799.
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This thesis consists of two papers devoted to the asymptotics of random matrix ensembles and measure valued stochastic processes which can be considered as generalizations of the Gaussian unitary ensemble (GUE) of Hermitian matrices H=A+A†, where the entries of A are independent identically distributed (iid) centered complex Gaussian random variables. In the first paper, a system of interacting diffusing particles on the real line is studied; special cases include the eigenvalue dynamics of matrix-valued Ornstein-Uhlenbeck processes (Dyson's Brownian motion). It is known that the empirical measure process converges weakly to a deterministic measure-valued function and that the appropriately rescaled fluctuations around this limit converge weakly to a Gaussian distribution-valued process. For a large class of analytic test functions, explicit formulae are derived for the mean and covariance functionals of this fluctuation process. The second paper concerns a family of random matrix ensembles interpolating between the GUE and the Ginibre ensemble of n x n matrices with iid centered complex Gaussian entries. The asymptotic spectral distribution in these models is uniform in an ellipse in the complex plane, which collapses to an interval of the real line as the degree of non-Hermiticity diminishes. Scaling limit theorems are proven for the eigenvalue point process at the rightmost edge of the spectrum, and it is shown that a non-trivial transition occurs between Poisson and Airy point process statistics when the ratio of the axes of the supporting ellipse is of order n -1/3.Denna avhandling består av två vetenskapliga artiklar som handlar om gränsvärdessatser för slumpmatriser och måttvärda stokastiska processer. De modeller som studeras kan betraktas som generaliseringar av den gaussiska unitära ensembeln (GUE) av hermiteska n x n-matriser H=A+A†, där A är en matris vars element är oberoende, likafördelade, centrerade, komplexa normalfördelade stokastiska variabler. I artikel I betraktas ett system av växelverkande diffunderande partiklar på reella linjen, vissa specialfall av denna modell kan tolkas som egenvärdesdynamiken för matrisvärda Ornstein-Uhlenbeck-processer (Dysons brownska rörelse). Sedan tidigare är det känt att den empiriska måttprocessen konvergerar svagt mot en deterministisk måttvärd funktion och att fluktuationerna runt denna gräns, i lämplig skalning, konvergerer svagt mot en distributionsvärd gaussisk process. För en stor klass av analytiska testfunktioner härleds explicita formler för medelvärdes- och kovariansfunktionalerna för denna fluktuationsprocess. Artikel II behandlar en familj av slumpmatrisensembler som interpolerar mellan GUE och Ginibre-ensembeln, bestående av matriser A som ovan. För denna modell är egenvärdena komplexa och asymptotiskt likformigt fördelade i en ellips i komplexa planet. Skalningsgränsvärdessatser för egenvärdet med maximal realdel och för egenvärdespunktprocessen kring detta visas för ett allmänt val av interpolationsparametern i modellen. Då förhållandet mellan axlarna i den asymptotiska ellipsen är av storleksordning n-1/3 uppträder en övergångsfas mellan Airypunktprocess- och Poissonprocessbeteendena, typiska för GUE respektive Ginibre-ensembeln.
QC 20100705
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Goupee, Andrew J. "Multiscale Investigation of Random Heterogenous Media in Materials and Earth Sciences." Fogler Library, University of Maine, 2010. http://www.library.umaine.edu/theses/pdf/GoupeeAJ2010.pdf.
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Tartakovsky, Daniel. "Prediction of transient flow in random porous media by conditional moments." Diss., The University of Arizona, 1996. http://etd.library.arizona.edu/etd/GetFileServlet?file=file:///data1/pdf/etd/azu_e9791_1996_263_sip1_w.pdf&type=application/pdf.
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Lai, Zhong Yuan [Verfasser]. "Wave dynamics in random, absorptive or laseractive media / Zhong Yuan Lai." Bonn : Universitäts- und Landesbibliothek Bonn, 2017. http://d-nb.info/1127666320/34.
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Ao, Chi On 1970. "Electromagnetic wave scattering by discrete random media with remote sensing applications." Thesis, Massachusetts Institute of Technology, 2001. http://hdl.handle.net/1721.1/16782.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2001.Includes bibliographical references (p. 171-182).
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
The scattering of electromagnetic waves in medium with randomly distributed discrete scatterers is studied. Analytical and numerical solutions to several problems with implications for the active and passive remote sensing of the Earth environment are obtained. The quasi-magnetostatic (QMS) solution for a conducting and permeable spheroid under arbitrary excitation is presented. The spheroid is surrounded by a weakly conducting background medium. The magnetic field inside the spheroid satisfies the vector wave equation, while the magnetic field outside can be expressed as the gradient of the Laplace solution. We solve this problem exactly using the separation of variables method in spheroidal coordinates by expanding the internal field in terms of vector spheroidal wavefunctions. The exact formulation works well for low to moderate frequencies; however, the solution breaks down at high frequency due to numerical difficulty in computing the spheroidal wavefunctions. To circumvent this difficulty, an approximate theory known as the small penetration-depth approximation (SPA) is developed. The SPA relates the internal field in terms of the external field by making use of the fact that at high frequency, the external field can only penetrate slightly into a thin skin layer below the surface of the spheroid. For spheroids with general permeability, the SPA works well at high frequency and complements the exact formulation. However, for high permeability, the SPA is found to give accurate broadband results. By neglecting mutual interactions, the QMS frequency response from a collection of conducting and permeable spheroids is also studied.
(cont.) In a dense medium, the failure to properly take into account of multiple scattering effects could lead to significant errors. This has been demonstrated in the past from extensive theoretical, numerical, and experimental studies of electromagnetic wave scattering by densely packed dielectric spheres. Here, electromagnetic wave scattering by dense packed dielectric spheroids is studied both numerically through Monte Carlo simulations and analytically through the quasi-crystalline approximation (QCA) and QCA with coherent potential (QCA-CP). We assume that the spheroids are electrically small so that single-particle scattering is simple. In the numerical simulations, the Metropolis shuffling method is used to generate realizations of configurations for non-interpenetrable spheroids. The multiple scattering problem is formulated with the volume integral equation and solved using the method of moments with electrostatic basis functions. General expressions for the self-interaction elements are obtained using the low-frequency expansion of the dyadic Green's function, and radiative correction terms are included. Results of scattering coefficient, absorption coefficient, and scattering matrix for spheroids in random and aligned orientation configurations are presented. It is shown that independent scattering approximation can give grossly incorrect results when the fractional volume of the spheroids is appreciable.
(cont.) In the analytical approach, only spheroids in the aligned configuration are solved. Low-frequency QCA and QCA-CP solutions are obtained for the average Green's function and the effective permittivity tensor. For QCA-CP, the low-frequency expansion of the uniaxial dyadic Green's function is required. The real parts of the effective permittivities from QCA and QCA-CP are compared with the Maxwell-Garnett mixing formula. ...
by Chi On Ao.
Ph.D.
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Veysoglu, Murat Emre. "Direct and inverse scattering models for random media and rough sufraces." Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/17375.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1994.Includes bibliographical references (p. 191-198).
by Murat Emre Veysoglu.
Ph.D.
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Zhang, Jinmiao. "A Hybrid Finite Element Method for Heterogeneous Media With Random Microstructures /." The Ohio State University, 1995. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487931512621134.
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Song, Yilang. "The influence of random microstructure on wave propagation through heterogeneous media." Thesis, University of Sheffield, 2015. http://etheses.whiterose.ac.uk/10160/.
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In this thesis the influence of mechanical and geometrical properties of a heterogeneous periodic composite material (in 1D and 2D), both deterministic and stochastic in nature, on wave propagation has been analysed from the position of stop band phenomenon. Numerical analyses have been used to identify those parameters that have the most significant effect on the wave filtering properties of the medium. The study has started on a 1D periodic laminate material. Further, a randomness has been added into the material’s properties in order to study its influence on the stop band. The stop band phenomenon has also been studied on the material in a 2D case, first with periodic microstructure, then with randomness added into the microstructure to test its influence on the stop band. Special attention has been given to the prediction of the first stop band frequency with numerical analysis of an explicitly defined heterogeneous structure compared and confirmed by results obtained using gradient theory and analytical derivations.
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Powell, Ellen Grace. "Scaling limits of critical systems in random geometry." Thesis, University of Cambridge, 2017. https://www.repository.cam.ac.uk/handle/1810/270147.
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This thesis focusses on the properties of, and relationships between, several fundamental objects arising from critical physical models. In particular, we consider Schramm--Loewner evolutions, the Gaussian free field, Liouville quantum gravity and the Brownian continuum random tree. We begin by considering branching diffusions in a bounded domain $D\subset$ $R^{d}$, in which particles are killed upon hitting the boundary $\partial D$. It is known that such a system displays a phase transition in the branching rate: if it exceeds a critical value, the population will no longer become extinct almost surely. We prove that at criticality, under mild assumptions on the branching mechanism and diffusion, the genealogical tree associated with the process will converge to the Brownian CRT. Next, we move on to study Gaussian multiplicative chaos. This is the rigorous framework that allows one to make sense of random measures built from rough Gaussian fields, and again there is a parameter associated with the model in which a phase transition occurs. We prove a uniqueness and convergence result for approximations to these measures at criticality. From this point onwards we restrict our attention to two-dimensional models. First, we give an alternative, ``non-Gaussian" construction of Liouville quantum gravity (a special case of Gaussian multiplicative chaos associated with the 2-dimensional Gaussian free field), that is motivated by the theory of multiplicative cascades. We prove that the Liouville (GMC) measures associated with the Gaussian free field can be approximated using certain sequences of ``local sets" of the field. This is a particularly natural construction as it is both local and conformally invariant. It includes the case of nested CLE$_{4}$, when it is coupled with the GFF as its set of ``level lines". Finally, we consider this level line coupling more closely, now when it is between SLE$_{4}$ and the GFF. We prove that level lines can be defined for the GFF with a wide range of boundary conditions, and are given by SLE$_{4}$-type curves. As a consequence, we extend the definition of SLE$_{4}(\rho)$ to the case of a continuum of force points.
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Lhermitte, Julien. "Using coherent small angle xray scattering to measure velocity fields and random motion." Thesis, McGill University, 2011. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=104825.
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The dynamics of cross-linked polymers under stress, such as those thatmake up rubber, are still not well understood. A combination of coherent xrayhomodyne and heterodyne techniques is used in order to measure fluctuations of the system when stretched. The combination of both techniques allows for the measurement of flow patterns, as well as the random nature of the system. After data analysis, the results show that the measurements successfully captured this flow information. The flow velocity was discovered to have a time-dependent nature similar to that of the stress-strain curve. After the flow velocity was extracted, the random nature of the system was analysed. This random motion was discovered not to be dominated by conventional diffusion, but some slower random process.La dynamique de polymères réticulés de stress, telles que celle qui compose le caoutchouc, n'est pas encore bien comprise. Une combinaison de techniques homodynes et hétérodynes de rayons x coherentes est utilisé pour mesurer les fluctuations du système, une fois étiré. La combinaison des deux techniques permet la mesure des régimes d'écoulement, ainsi que le caractère aléatoire du système. Après l'analyse des données, les résultats montrent que les mesures ont réussi à capturer cet information. La vitesse d'écoulement a été découverte de contenir une nature en fonction du temps semblable à celle de la courbe contrainte-déformation. Après la vitesse d'écoulement a été extraite, la nature aléatoire du système a été analysé. Cette motion a été découverte au hasard de ne pas être dominé par la diffusion classique, mais de certains processus aléatoires plus lents.
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Uda, Kenneth O. "A qualitative approach to the existence of random periodic solutions." Thesis, Loughborough University, 2015. https://dspace.lboro.ac.uk/2134/17355.
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In this thesis, we study the existence of random periodic solutions of random dynamical systems (RDS) by geometric and topological approach. We employed an extension of ergodic theory to random setting to prove that a random invariant set with some kind of dissipative structure, can be expressed as union of random periodic curves. We extensively characterize the dissipative structure by random invariant measures and Lyapunov exponents. For stochastic flows induced by stochastic differential equations (SDEs), we studied the dissipative structure by two point motion of the SDE and prove the existence exponential stable random periodic solutions.
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Sukop, Michael C. "POROSITY, PERCOLATION THRESHOLDS, AND WATER RETENTION BEHAVIOR OF RANDOM FRACTAL POROUS MEDIA." UKnowledge, 2001. http://uknowledge.uky.edu/gradschool_diss/459.
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Fractals are a relatively recent development in mathematics that show promise as a foundation for models of complex systems like natural porous media. One important issue that has not been thoroughly explored is the affect of different algorithms commonly used to generate random fractal porous media on their properties and processes within them. The heterogeneous method can lead to large, uncontrolled variations in porosity. It is proposed that use of the homogeneous algorithm might lead to more reproducible applications. Computer codes that will make it easier for researchers to experiment with fractal models are provided. In Chapter 2, the application of percolation theory and fractal modeling to porous media are combined to investigate percolation in prefractal porous media. Percolation thresholds are estimated for the pore space of homogeneous random 2-dimensional prefractals as a function of the fractal scale invariance ratio b and iteration level i. Percolation in prefractals occurs through large pores connected by small pores. The thresholds increased beyond the 0.5927 porosity expected in Bernoulli (uncorrelated) networks. The thresholds increase with both b (a finite size effect) and i. The results allow the prediction of the onset of percolation in models of prefractal porous media. Only a limited range of parameters has been explored, but extrapolations allow the critical fractal dimension to be estimated for many b and i values. Extrapolation to infinite iterations suggests there may be a critical fractal dimension of the solid at which the pore space percolates. The extrapolated value is close to 1.89 -- the well-known fractal dimension of percolation clusters in 2-dimensional Bernoulli networks. The results of Chapters 1 and 2 are synthesized in an application to soil water retention in Chapter 3.